text: The Stuart–Landau equation describes the behavior of a nonlinear oscillating system near the Hopf bifurcation, named after John Trevor Stuart and Lev Landau. In 1944, Landau proposed an equation for the evolution of the magnitude of the disturbance, which is now called as the Landau equation, to explain the transition to turbulence based on a phenomenological argument and an attempt to derive this equation from hydrodynamic equations was done by Stuart for plane Poiseuille flow in 1958. The formal derivation to derive the Landau equation was given by Stuart, Watson and Palm in 1960. The perturbation in the vicinity of bifurcation is governed by the following equation
  where 
  * is a complex quantity describing the disturbance,
  * is the complex growth rate,
  * is a complex number and  is the Landau constant.
  The evolution of the actual disturbance is given by the real part of  i.e.,  by . Here the real part of the growth rate is taken to be positive, i.e.,  because otherwise the system is stable in the linear sense, that is to say, for infinitesimal disturbances ( is a small number), the nonlinear term in the above equation is negligible in comparison to the other two terms in which case the amplitude grows in time only if . The Landau constant is also taken to be positive,  because otherwise the amplitude will grow indefinitely (see below equations and the general solution in the next section). The Landau equation is the equation for the magnitude of the disturbance,
  which can also be re-written as
  Similarly, the equation for the phase is given by
  For non-homogeneous systems, i.e., when  depends on spatial coordinates, see Ginzburg–Landau equation. Due to the universality of the equation, the equation finds its application in many fields such as hydrodynamic stability, Belousov–Zhabotinsky reaction, etc.